Interaction of oblique waves with an ice sheet over an asymmetric trench

Abstract

A model for oblique wave scattering by an asymmetric trench beneath a large floating ice sheet is studied using linearized water wave theory. Eigenfunction expansion method have been used to calculate the velocity potential explicitly for the associated boundary value problem. Using condition along the boundaries of the trench a set of integral equations are formed. The solutions of the integral equations are obtained by using multi-term Galerkin approximations with suitably chosen basis functions involving ultraspherical Gegenbauer polynomials. Analytic solution for the reflection and transmission coefficients are obtained and analyzed numerically for a number of figures. The role of thin ice sheet on wave scattering in marginal ice zone is studied by analyzing the reflection and transmission coefficients for a set of parameters such as flexural rigidity of ice, angle of incidence, depth and width of the asymmetric trench. We observe that wave reflection decreases in an oscillatory manner with the increase in the dimensionless flexural rigidity parameter. The correctness of the present method is confirmed by comparing the results available in the literatures. The problem here is to understand how the flexural gravity waves propagate over an asymmetric submarine trench in such an ice field.